Viscous micropump of immiscible fluids using magnetohydrodynamic effects and a power-law conducting fluid


  • Juan Rolando Gómez López Instituto Politécnico Nacional
  • Clara Guadalupe Hernández Roblero Universidad Tecnológica de México
  • Juan Pablo Escandón Colin Instituto Politécnico Nacional
  • René Osvaldo Vargas Aguilar Instituto Politécnico Nacional



Micropump, non-Newtonian fluid, immiscible fluids, magnetohydrodynamics, parallel flat plates microchannel.


Small-scale fluid transport methods have grown significantly in recent years, mainly in applications in microfluidic systems. Therefore, the present study analyzes the movement of two-layers of immiscible fluids within a parallel flat plates microchannel. The fluid layers are composed of a Newtonian fluid and a power-law fluid. The pumping is produced by magnetohydrodynamics effects that act on the non-Newtonian conducting fluid dragging the non-conducting Newtonian fluid by viscous forces. Under the consideration of a laminar, incompressible, and unidirectional flow, the dimensionless mathematical model is established by the momentum equations for each fluid, together with the corresponding boundary conditions at solid-liquid and liquid-liquid interfaces. The problem formulation is semi-analytically solved using the Newton-Raphson method. The results are presented as a function of the velocity profiles and flow rate, showing interesting behaviors that depend on the physical and electrical properties of each fluid and flow conditions via the dimensionless parameters such as the flow behavior index, a magnetic parameter related to Lorenz forces, the fluids viscosity ratios and the dimensionless liquid-liquid interface position. This work contributes to the understanding of the various immiscible non-conducting fluids pumping techniques that can be used in microdevices.

Author Biographies

Juan Rolando Gómez López, Instituto Politécnico Nacional

Mechanical Engineer by the Instituto Politécnico Nacional at México. Student of Master Degree in Thermofluids at the Escuela Superior de Ingeniería Mecánica y Eléctrica of Instituto Politécnico Nacional at Mexico. Research in electrokinetic flows and magnetohydrodynamic flows, transport phenomena in fluid flows, micropumps and fluids rheology. One publication in a Journal registered in the Journal Citation Reports of the Thomson Reuters.

Clara Guadalupe Hernández Roblero, Universidad Tecnológica de México

Mechanical Engineer and MSc in Thermofluids by the Instituto Politécnico Nacional at México. Currently, professor and researcher at the Universidad Tecnológica de México –UNITEC MÉXICO- Campus Marina-Cuitláhuac at Mexico. Research in electrokinetic and magnetohydrodynamic flows, transport phenomena in heat transfer and fluid flows, micropumps, micromixers, and fluids rheology. Three publications in Journals registered in the Journal Citation Reports of the Thomson Reuters.

Juan Pablo Escandón Colin, Instituto Politécnico Nacional

Mechanical Engineer and MSc in Mechanical Engineering by the Instituto Politécnico Nacional at México. Doctorate in Engineering by the Universidad Nacional Autónoma de México in Mexico.  Currently, professor and researcher at the Escuela Superior de Ingeniería Mecánica y Eléctrica of the Instituto Politécnico Nacional at Mexico. Research in electrokinetic and magnetohydrodynamic flows, transport phenomena in heat transfer and fluid flows, micropumps, micromixers, and fluids rheology. Fifteen publications in Journals registered in the Journal Citation Reports of the Thomson Reuters.

René Osvaldo Vargas Aguilar, Instituto Politécnico Nacional

Chemical Engineer, MSc in Chemical Engineering and PhD in Engineering by the National Autonoumus University of Mexico. Full time professor since 2009 at Escuela Superior de Ingeniería Mecánica y Eléctrica of the National Polytechnic Institute of Mexico. Research interests in non-Newtonian fluid mechanics, complex fluids, polymer processing and computational fluid dynamics.


U. M¨uller and L. B¨uhler, Magnetofluiddynamics in Channels and Containers (Springer, Berlin-Heidelberg, 2001),

P.A. Davidson, An Introduction to Magnetohydrodynamics (Cambridge Univerity Press, New York, U.S., 2001).

R. J. Moreau, Magnetohydrodynamics (Springer, Dordrecht, 1990),

O.M. Al-Habahbeh, M. Al-Saqqa, M. Safi and T. Abo Khater, Review of magnetohydrodynamic pump applications, Alex. Eng. J. 55 (2016) 1347,

V. Patel and S.K. Kassegne, Electroosmosis and thermal effects in magnetohydrodynamic (MHD) micropumps using 3D MHD equations, Sens. Actuator B-Chem. 122 (2007) 42,

I. Dolezel, V. Kotlan, B. Ulrych and V. Valenta, Magnetohydrodynamic pumps with permanent magnets for pumping molten metals or salts, Electroscope 2009 (2009) 86.

I. Dolezel, V. Kotlan and B. Ulrych, Magnetohydrodynamic pumps for molten salts in cooling loops of high-temperature nuclear reactors, Prz. Elektrotech. 2011 (2011) 28.

H. Kabbani, A. Wang, X. Luo, and S. Qian, Modeling Redoxbased magnetohydrodynamics in three-dimensional microfluidic channels, Phys. Fluids 19 (2007) 083604,

C. Kleinstreuer, Microfluidics and Nanofluidics. Theory and Selected Applications (Wiley, New Jersey, 2013),

D. Li, Encyclopedia of Microfluidics and Nanofluidics (Springer, Boston, 2008).

A. Homsy et al., A high current density DC magnetohydrodynamic (MHD) micropump, Lab Chip 5 (2005) 466,

H. S. Kabbani, M. J. Mack, S. W. Joo and S. Qian, Analytical prediction of flow field in magnetohydrodynamic-based microfluidic devices, J. Fluids Eng.-Trans. ASME 130 (2008) 091204,

F. E. H. Tay, Microfluidics and BioMEMS Applications (Springer, Boston, 2002).

S. Lim and B. Choi, A study on the MHD (magnetohydrodynamic) micropump with side-walled electrodes, J. Mech. Sci. Technol. 23 (2009) 739,

L. Huang, W. Wang, M.C. Murphy, K. Lian and Z.-G. Ling, LIGA fabrication and test of a DC type magnetohydrodynamic (MHD) micropump, Microsyst. Technol. 6 (2000) 235,

D. Chatterjee and S. Amiroudine, Lattice Boltzmann simulation of thermofluidic transport phenomena in a DC magnetohydrodynamic

(MHD) micropump, Biomed. Microdevices 13 (2011) 147,

H. H. Bau, J. Zhu, S. Qian and Y. Xiang, A magnetohydrodynamically controlled fluidic network, Sens. Actuator B Chem. 88 (2003) 205,

M. Rivero and S. Cuevas, Analysis of the slip condition in magnetohydrodynamic (MHD) micropumps, Sens. Actuator B Chem. 166-167 (2012) 884,

J. Azimi-Boulali, M. Zakeri and M. Shoaran, A study on the 3D fluid flow of MHD micropump, J. Braz. Soc. Mech. Sci. Eng. 41 (2019) 478,

S. Moghaddam, Investigating flow in MHD micropumps, SN Appl. Sci. 1 (2019) 1609,

Y. Jian and L. Chang, Electromagnetohydrodynamic (EMHD) micropumps under a spatially non-uniform magnetic field, AIP Adv. 5 (2015) 057121,

P. K. Mondal and S. Wongwises, Magneto-hydrodynamic (MHD) micropump of nanofluids in a rotating microchannel under electrical double-layer effect, Proc. Inst. Mech. Eng. E 234 (2020) 318,

S. Moghaddam, MHD micropumping of power-law fluids: A numerical solution, Korea Aust. Rheol. J. 25 (2013) 29,

M. Pourjafar, F. Malmir, S. Bazargan and K. Sadeghy, Magnetohydrodynamic flow of Bingham fluids in a plane channel: A theoretical study, J. Non-Newton. Fluid Mech. 264 (2019) 1, 005.

Y. A. Elmaboud and S. I. Abdelsalam, DC/AC magnetohydrodynamic-micropump of a generalized Burger’s fluid in an annulus, Phys. Scr. 94 (2019) 115209,

A. Shahidian et al., Flow analysis of non-Newtonian blood in a magnetohydrodynamic pump, IEEE Trans. Magn. 45 (2009) 2667,

F.-Q. Li, Y.-J. Jian, Z.-Y. Xie, and L. Wang, Electromagnetohydrodynamic flow of Powell-Eyring fluids in a narrow confinement, J. Mech. 33 (2017) 225,

R. Shail, On laminar two-phase flows in magnetohydrodynamics, Int. J. Eng. Sci. 11 (1973) 1103,

J. Lohrasbi and V. Sahai, Magnetohydrodynamic heat transferin two-phase flow between parallel plates, Appl. Sci. Res. 45 (1988) 53,

J. C. Umavathi, A. Mateen, A.J. Chamka and A. Al-Mudhaf, Oscillatory Hartmann two-fluid flow and heat transfer in a horizontal channel, Int. J. Appl. Mech. Eng. 11 (2006) 155.

A. Mateen, Magnetohydrodynamic flow and heat transfer of two immiscible fluids through a horizontal channel, Int. J. Curr. Eng. Technol. 3 (2013) 1952.

Z. Abbas and J. Hasnain, Two-phase magnetoconvection flow of magnetite (Fe3O4) nanoparticles in a horizontal composite porous annulus, Res. Phys. 7 (2017) 574,

Z. Abbas, J. Hasnain and M. Sajid, Hydromagnetic mixed convective two-phase flow of couple stress and viscous fluids in an inclined channel, Z. Naturforsch. A 69 (2014) 553,

M. S. Malashetty and J. C. Umavathi, Two-phase magnetohydrodynamic flow and heat transfer in an inclined channel, Int. J. Multiph. Flow 23 (1997) 545,

M. S. Malashetty, J. C. Umavathi, and J. P. Kumar, Magnetoconvection of two-immiscible fluids in vertical enclosure, Heat Mass Transf. 42 (2006) 977,

D. Nikodijevic, D. Milenkovic and Z. Stamenkovic, MHD Couette two-fluid flow and heat transfer in presence of uniform inclined magnetic field, Heat Mass Transf. 47 (2011) 1525,

P. Chanturani and S.S. Bharatiya, Two layered magnetohydrodynamic flow through parallel plates with applications, Indian J. Pure Appl. Math. 32 (2001) 55.

A. Brask, G. Goranovi´c, M.J. Jensen and H. Bruus, A novel electro-osmotic pump design for nonconducting liquids: theoretical analysis of flow rate-pressure characteristics and stability, J. Micromech. Microeng. 15 (2005) 883,

Y. Gao, T. N. Wong, C. Yang and K. T. Ooi, Transient twoliquid electroosmotic flow with electric charges at the interface, ColloidS Surf. A. 266 (2005) 117,

G. D. Ngoma and F. Erchiqui, Pressure gradient and electroosmotic effects on two immiscible fluids in a microchannel between

two parallel plates, J. Micromech. Microeng. 16 (2006) 83,

M. Liu and J. Yang, Electrokinetic effect of the endothelial glycocalyx layer on two-phase blood flow in small blood vessels, Microvas. Res. 78 (2009) 14,

A. M. Afonso, M. A. Alves and F. T. Pinho, Analytical solution of two-fluid electro-osmotic flows of viscoelastic fluids, J. Colloid Interface Sci. 395 (2013) 277,

Y. Huang, H. Li and T.N. Wong, Two immiscible layers of electro-osmotic driven flow with a layer of conducting non-Newtonian fluid, Int. J. Heat Mass Transf. 74 (2014) 368,

K. M. Joshep, A. Peter, P. E. Asie and S. Usman, The unsteady MHD free convective two immiscible fluid flows in a horizontal channel with heat and mass transfer, Int. J. Math. Comput. Res. 3 (2015) 954.

D. Nikodijevi´c, ˇ Z. Stamenkovi´c, D. Milenkovi´c, B. Blagojevi´c and J. Nikodijevi´c, Flow and heat transfer of two immiscible fluids the presence of uniform inclined magnetic field, Math. Probl. Eng. 2011 (2011) 132302,

A. Z. Szeri, Fluid Film Lubrication 2nd ed. (Cambridge University Press, Cambridge, 2010),

G. W. Sutton and A. Sherman, Engeneering Magnetohydrodynamics (Dover Publications, New York, 2006).

A. Ramos, Electrohydrodynamic and magnetohydrodynamic micro- pumps, in: S. Hardt, F. Sch¨onfeld (Eds.), Microfluidic Technologies for Miniaturized Analysis Systems (Springer, Boston, 2007). 2.

H. Kim, H. Hwang, S. Baek and D. Kim, Design, fabrication and performance evaluation of a printed-circuit-board microfluidic electrolytic pump for lab-on-a-chip devices, A. Phys. 277 (2018) 73,

A. Homsy, Ph.D. thesis, University of Neuchˆatel, 2006.

H.-L. Zhang and S. J. Han, Viscosity and density of water + sodium chloride + potassium chloride solutions at 298.15 K, J. Chem. Eng. Data 41 (1996) 516,

T. Isono, Density, viscosity, and electrolytic conductivity of concentrated aqueous electrolyte solutions at several temperatures. Alkaline-earth chlorides, lanthanum chloride, sodium chloride, sodium nitrate, sodium bromide, potassium nitrate, potassium bromide, and cadmium nitrate, J. Chem. Eng. Data 29 (1984) 45,

J. Kestin, H. Ezzat Khalifa and R. J. Correia, Tables of the dynamic and kinematic viscosity of aqueous KCI solutions in the temperature range 25-150 ±C and the pressure range 0.1-35 MPa, J. Phys. Chem. Ref. Data 10 (1981) 57,

Y. C. Wu, W. F. Koch and K. W. Pratt, Proposed new electrolytic conductivity primary standars for KCl solutions, J. Res. Natl. Inst. Stand. Technol. 96 (1991) 191,

H. Golnabi, M.R. Matloob, M. Bahar and M. Sharifian, Investigation of electrical conductivity of different water liquids and electrolyte solutions, Iran. Phys. J. 3 (2009) 24,

S. Qian and H. H. Bau, Magneto-hydrodynamics based microfluidics, Mech. Res. Commun. 36 (2009) 10,

F. A. Morrison, Undestanding Rheology (Oxford University Press, Oxford, 2001).

R. W. Flumerfelt, W. M. Pierick, S. L. Cooper and R. B. Bird, Generalized plane Couette flow of a non-Newtonian fluid, Ind. Eng. Chem. Fundamen. 8 (1969) 354,

J.D. Hoffman, Numerical Methods for Engineers and Scientists (Marcel Dekker, New York 2001).

J. Jang and S. S. Lee, Theoretical and experimental study of MHD (magnetohydrodynamic) micropump, Sens. Actuator A-Phys. 80 (2000) 84,

Z. P. Aguilar, P. Arumugam and I. Fritsch, Study of magnetohydrodynamic driven flow through LTCC channel with self-contained electrodes, J. Electroanal. Chem. 591 (2006) 201,




How to Cite

J. R. Gómez López, C. G. Hernández Roblero, J. P. Escandón Colin, and R. O. Vargas Aguilar, “Viscous micropump of immiscible fluids using magnetohydrodynamic effects and a power-law conducting fluid”, Rev. Mex. Fís., vol. 67, no. 6 Nov-Dec, pp. 060601 1–, Nov. 2021.